What is x^2-4y^2-2x+16y-31=0 ?

The solution to x^2-4y^2-2x+16y-31=0 is Hyperbola with (h,k)=(1,2),a=4,b=2

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x^2-4y^2-2x+16y-31=0

x^{2} - 4 y^{2} - 2 x + 16 y - 31 = 0

(h, k) = (1, 2), a = 4, b = 2

Solution steps

x^{2} - 4 y^{2} - 2 x + 16 y - 31 = 0

Rewrite

x^{2} - 4 y^{2} - 2 x + 16 y - 31 = 0

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{4 ^{2}} - \frac{( y - 2 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, 2), a = 4, b = 2

x^{2} - 64 y^{2} = 64

\frac{36 ( x - 7 ) ^{2} - 64 ( y - 6 ) ^{2}}{2304} = 1

(y - 4)^{2} = \frac{4 ( x + 1 ) ^{2} + 84}{3}

3 (x + \frac{1}{3})^{2} - 3 (y - \frac{7}{3})^{2} = - 40

3 x^{2} - y^{2} = 25

What is x^2-4y^2-2x+16y-31=0 ?
The solution to x^2-4y^2-2x+16y-31=0 is Hyperbola with (h,k)=(1,2),a=4,b=2